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Momentum and Impulse Momentum = mass x velocity p = mv units: kg·m/s ***momentum is a vector quantity Conceptually, momentum is a characteristic of motion that reflects how difficult it would be to stop the moving object Impulse(change in momentum) = Force x time: Δp = FΔt units: N·s A net force applied for a given time interval will result in a change in momentum…this is really Newton’s Second Law: F = ma F = mΔv/ Δt F Δt = Δ mv Sample Problem • A 1400 kg car moving westward with a velocity of 15 m/s collides with a utility pole and is brought to rest in 0.30 s. Find the force exerted on the car during the collision. Conservation of Momentum • Keep in mind… – The individual objects in a collision can, and do, change momentum – Two objects colliding experience equal force for equal time, thus the magnitude of impulse, or change in momentum, must be the same for both objects – When there are no external influences, momentum gained by one object must equal the momentum lost by another and the total momentum of the system is constant Conservation of Momentum • Whenever objects interact in the absence of external forces, the net momentum of the objects before the interaction equals the net momentum of the objects after the interaction. Σp before = Σp after ***This general relationship will take on different appearances when applied to different situations Types of collisions • Perfectly Inelastic Collision (Sticky): A collision in which two objects stick together and move with a common velocity after colliding • For 2 objects colliding inelastically… Σp before = Σp after m1v1+m2v2=(m1+m2)vf In these collisions, some kinetic energy is lost in the form of heat and sound as the objects deform during the collision Types of collisions • Perfectly Elastic Collision (bouncy) : A collision in which the total momentum and the total kinetic energy remain constant • After the collision, the two objects move independently • For 2 objects colliding elastically… Σp before = Σp after m1v1i + m2v2i = m1v1f + m2v2f and ΣKEbefore = ΣKEafter ½ m1v1i2 + ½ m2v2i2 = ½ m1v1f2 + ½ m2v2f2 In Real life… • Only particle collisions are truly elastic, however, many collisions are close enough to be approximated as elastic (ie…billiard balls) • Macroscopic collisions are somewhere along a continuum of between being elastic and perfectly inelastic Practice #1 • A 0.015 kg marble moving to the right at 0.225 m/s makes an elastic head-on collision with a 0.030 kg marble moving to the left at 0.180 m/s. After the collision, the smaller marble moves to the left at 0.315 m/s. What is the velocity of the 0.030 kg marble after the collision? Practice #2 • A 1850 kg luxury sedan stopped at a traffic light is struck from the rear by a compact car with a mass of 975 kg. The two cars become entangled as a result of the collision. If the compact car was moving at a velocity of 22.0 m/s to the north before the collision, what is the velocity of the entangled mass after the collision? Practice #3 • A 76 kg boater, initially at rest in a stationary 45 kg boat, steps out of the boat and onto the dock. IF the boater moves out of the boat with a velocity of 2.5 m/s to the right, what is the final velocity of the boat?